| Load | 100 kW | 100 kW and 50 kVAR |
|---|---|---|
| Power consumed by the load (kW) | 100 | 100 |
| Current (A) | 57.8 | 64.6 |
| Line losses (kW) | 33.4 | 41.6 |
| Voltage drop along line (V) | 817 | 913 |
| Required delivery voltage at generating end (V) | 1680 | 1892 |
The above examples show that there is a considerable demand placed on the generator to operate the various loads on a system. In reality, the generator terminal voltage Vs is constant, plus or minus 5% by design. As the load increases or decreases, the current from the generator changes significantly and the voltage drop on the system Vload requires compensation (Figure 1.3-8). Therefore, the second major function of the generator, after production of “real” power, is to produce “reactive” power to help control the voltage on the grid, which will also be discussed later in Chapter 4.
Figure 1.3-8 The effect on the voltage drop as the circuit goes from lagging through unity to leading power factor operation.
1.4 THREE‐PHASE CIRCUITS
The two‐wire AC circuits discussed above (called single‐phase circuits or systems), are commonly used in residential, commercial, low voltage, and low power industrial applications. However, all electric power systems to which industrial generators are connected are three‐phase systems. Therefore, any discussion in this book about the “power system” will refer to a three‐phase system. Moreover, in industrial applications, the voltage supplies are, for all practical reasons, balanced, meaning that all three‐phase voltages are equal in magnitude and apart by 120 electrical degrees. In those rare events in which the voltages are unbalanced, the implications for the operation of the generator will be discussed in other chapters of this book.
Three‐phase electric systems may have a fourth wire, called “neutral.” The “neutral” wire of a three‐phase system will conduct electricity if the source and/or the load are unbalanced. In three‐phase systems, two sets of voltages and currents can be identified. These are the phase and line voltages and currents.
Figure 1.4-1 shows the main elements of a three‐phase circuit. Three‐phase circuits can have their sources and/or loads connected in wye (also known as “star”) or in delta forms. (See Figure 1.4-2 for a wye‐connected source feeding a delta‐connected load.)
Figure 1.4-1 Three‐phase systems. Schematic depiction of a three‐phase circuit and the vector (phasor) diagram representing the currents, voltages, and angles between them.
Figure 1.4-2 A “wye‐connected” source feeding a “delta‐connected” load.
Almost without exception, hydro generators have their windings connected in wye (star) form. Therefore, in this book, the source (or generator) will be shown wye‐connected. There are a number of important reasons why hydro generators are wye‐connected. They have to do with considerations about its effective protection as well as design (insulation, grounding, etc.). These will be discussed in the chapters covering stator construction and operations.
On the other hand, loads can be found connected in wye, delta, or a combination of the two. This book is not about circuit solutions; therefore, the type of load connection will not be brought up herein.
1.5 BASIC PRINCIPLES OF MACHINE OPERATION
In Section 1.1, basic principles were presented showing how a current flowing in a conductor produces a magnetic field. In this section, three important laws of electromagnetism will be presented. These laws, together with the law of energy conservation, constitute the basic theoretical bricks on which the operation of an electrical machine is based.
1.5.1 Faraday's Law of Electromagnetic Induction
This basic law of Electromagnetic Induction, derived by the genius of the great English chemist and physicist Michael Faraday (1791–1867), presents itself in two different forms:
1 A moving conductor cutting the lines of force (flux) of a constant magnetic field has a voltage induced in it.
2 A changing magnetic flux inside a loop made from a conductor material will induce a voltage in the loop.
In both instances, the rate of change of the magnetic field is the critical determinant of the resulting voltage potential. Figure 1.5-1 illustrates both cases of electromagnetic induction and also provides the basic relationship between the changing flux and the voltage induced in the loop. The first case shows the relationship between the induced voltage in a wire moving across a constant field. The second case shows one of the simple rules that can be used to determine the direction of the induced voltage in the moving conductor.
Figure 1.5-1 Both forms of Faraday's basic law of electromagnetic induction. A simple rule (the “right‐hand” rule) is used to determine the direction of the induced voltage in a conductor moving across a magnetic field at a given velocity.
1.5.2 Ampere–Biot–Savart's Law
This basic law is attributed to the French physicists Andre Marie Ampere (1775–1836), Jean Baptiste Biot (1774–1862), and Victor Savart (1803–1862). In its simplest form, this law can be seen as the “reverse” of Faraday's law. Whereas Faraday's law predicts a voltage induced in a conductor moving across a magnetic field, the Ampere–Biot–Savart law establishes that a force is generated on a current‐carrying conductor located in a magnetic